import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns #importing all necessary Libraries
life_expectancy = pd.read_csv('/content/Life Expectancy Data.csv') #Reading the data set
life_expectancy.head() #gives top 5 rows with atrributes
life_expectancy.dropna(inplace=True) # drop rows with missing values

life_expectancy.dtypes

Country                             object
Year                                 int64
Status                              object
Life expectancy                    float64
Adult Mortality                    float64
infant deaths                        int64
Alcohol                            float64
percentage expenditure             float64
Hepatitis B                        float64
Measles                              int64
 BMI                               float64
under-five deaths                    int64
Polio                              float64
Total expenditure                  float64
Diphtheria                         float64
 HIV/AIDS                          float64
GDP                                float64
Population                         float64
 thinness  1-19 years              float64
 thinness 5-9 years                float64
Income composition of resources    float64
Schooling                          float64
dtype: object

life_expectancy.describe() #statistical summary of the arributes with numerical values

	Year	Life expectancy	Adult Mortality	infant deaths	Alcohol	percentage expenditure	Hepatitis B	Measles	BMI	under-five deaths	Polio	Total expenditure	Diphtheria	HIV/AIDS	GDP	Population	thinness 1-19 years	thinness 5-9 years	Income composition of resources	Schooling
count	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1649.000000	1.649000e+03	1649.000000	1649.000000	1649.000000	1649.000000
mean	2007.840509	69.302304	168.215282	32.553062	4.533196	698.973558	79.217708	2224.494239	38.128623	44.220133	83.564585	5.955925	84.155246	1.983869	5566.031887	1.465363e+07	4.850637	4.907762	0.631551	12.119891
std	4.087711	8.796834	125.310417	120.847190	4.029189	1759.229336	25.604664	10085.802019	19.754249	162.897999	22.450557	2.299385	21.579193	6.032360	11475.900117	7.046039e+07	4.599228	4.653757	0.183089	2.795388
min	2000.000000	44.000000	1.000000	0.000000	0.010000	0.000000	2.000000	0.000000	2.000000	0.000000	3.000000	0.740000	2.000000	0.100000	1.681350	3.400000e+01	0.100000	0.100000	0.000000	4.200000
25%	2005.000000	64.400000	77.000000	1.000000	0.810000	37.438577	74.000000	0.000000	19.500000	1.000000	81.000000	4.410000	82.000000	0.100000	462.149650	1.918970e+05	1.600000	1.700000	0.509000	10.300000
50%	2008.000000	71.700000	148.000000	3.000000	3.790000	145.102253	89.000000	15.000000	43.700000	4.000000	93.000000	5.840000	92.000000	0.100000	1592.572182	1.419631e+06	3.000000	3.200000	0.673000	12.300000
75%	2011.000000	75.000000	227.000000	22.000000	7.340000	509.389994	96.000000	373.000000	55.800000	29.000000	97.000000	7.470000	97.000000	0.700000	4718.512910	7.658972e+06	7.100000	7.100000	0.751000	14.000000
max	2015.000000	89.000000	723.000000	1600.000000	17.870000	18961.348600	99.000000	131441.000000	77.100000	2100.000000	99.000000	14.390000	99.000000	50.600000	119172.741800	1.293859e+09	27.200000	28.200000	0.936000	20.700000

life_expectancy.drop(['Country','Status'],inplace=True,axis=1) #not useful for the linear regression model.
life_expectancy

	Year	Life expectancy	Adult Mortality	infant deaths	Alcohol	percentage expenditure	Hepatitis B	Measles	BMI	under-five deaths	Polio	Total expenditure	Diphtheria	HIV/AIDS	GDP	Population	thinness 1-19 years	thinness 5-9 years	Income composition of resources	Schooling
0	2015	65.0	263.0	62	0.01	71.279624	65.0	1154	19.1	83	6.0	8.16	65.0	0.1	584.259210	33736494.0	17.2	17.3	0.479	10.1
1	2014	59.9	271.0	64	0.01	73.523582	62.0	492	18.6	86	58.0	8.18	62.0	0.1	612.696514	327582.0	17.5	17.5	0.476	10.0
2	2013	59.9	268.0	66	0.01	73.219243	64.0	430	18.1	89	62.0	8.13	64.0	0.1	631.744976	31731688.0	17.7	17.7	0.470	9.9
3	2012	59.5	272.0	69	0.01	78.184215	67.0	2787	17.6	93	67.0	8.52	67.0	0.1	669.959000	3696958.0	17.9	18.0	0.463	9.8
4	2011	59.2	275.0	71	0.01	7.097109	68.0	3013	17.2	97	68.0	7.87	68.0	0.1	63.537231	2978599.0	18.2	18.2	0.454	9.5
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2933	2004	44.3	723.0	27	4.36	0.000000	68.0	31	27.1	42	67.0	7.13	65.0	33.6	454.366654	12777511.0	9.4	9.4	0.407	9.2
2934	2003	44.5	715.0	26	4.06	0.000000	7.0	998	26.7	41	7.0	6.52	68.0	36.7	453.351155	12633897.0	9.8	9.9	0.418	9.5
2935	2002	44.8	73.0	25	4.43	0.000000	73.0	304	26.3	40	73.0	6.53	71.0	39.8	57.348340	125525.0	1.2	1.3	0.427	10.0
2936	2001	45.3	686.0	25	1.72	0.000000	76.0	529	25.9	39	76.0	6.16	75.0	42.1	548.587312	12366165.0	1.6	1.7	0.427	9.8
2937	2000	46.0	665.0	24	1.68	0.000000	79.0	1483	25.5	39	78.0	7.10	78.0	43.5	547.358878	12222251.0	11.0	11.2	0.434	9.8

1649 rows × 20 columns

def make_corr_heatmap(df): #function that plots correlation heatmap
  corr = df.corr()
  fig, ax = plt.subplots(figsize=(12,9))
  sns.heatmap(corr, annot=True)
  ax.set_xticklabels(ax.get_xticklabels())
  plt.show()

make_corr_heatmap(life_expectancy)
sns.pairplot(life_expectancy,diag_kind='kde') #displays pair plot with kernel density

<seaborn.axisgrid.PairGrid at 0x7e0c2d4d65f0>

#year,infant_deaths,measles,population,total_expenditure
print(life_expectancy.columns)
life_expectancy.drop(['Year','infant deaths','Measles ','Total expenditure','Population'],inplace=True,axis=1) #less correlation with life expectancy: redundant attritubes
#life_expectancy.isnull().count()

Index(['Year', 'Life expectancy ', 'Adult Mortality', 'infant deaths',
       'Alcohol', 'percentage expenditure', 'Hepatitis B', 'Measles ', ' BMI ',
       'under-five deaths ', 'Polio', 'Total expenditure', 'Diphtheria ',
       ' HIV/AIDS', 'GDP', 'Population', ' thinness  1-19 years',
       ' thinness 5-9 years', 'Income composition of resources', 'Schooling'],
      dtype='object')

X=life_expectancy.drop('Life expectancy ',axis=1)
Y=life_expectancy['Life expectancy ']
print(X,Y)

#split the dataset into training and testing sets to then train a linear regression model using scikit-learn.

      Adult Mortality  Alcohol  percentage expenditure  Hepatitis B   BMI   \
0               263.0     0.01               71.279624         65.0   19.1   
1               271.0     0.01               73.523582         62.0   18.6   
2               268.0     0.01               73.219243         64.0   18.1   
3               272.0     0.01               78.184215         67.0   17.6   
4               275.0     0.01                7.097109         68.0   17.2   
...               ...      ...                     ...          ...    ...   
2933            723.0     4.36                0.000000         68.0   27.1   
2934            715.0     4.06                0.000000          7.0   26.7   
2935             73.0     4.43                0.000000         73.0   26.3   
2936            686.0     1.72                0.000000         76.0   25.9   
2937            665.0     1.68                0.000000         79.0   25.5   

      under-five deaths   Polio  Diphtheria    HIV/AIDS         GDP  \
0                     83    6.0         65.0        0.1  584.259210   
1                     86   58.0         62.0        0.1  612.696514   
2                     89   62.0         64.0        0.1  631.744976   
3                     93   67.0         67.0        0.1  669.959000   
4                     97   68.0         68.0        0.1   63.537231   
...                  ...    ...          ...        ...         ...   
2933                  42   67.0         65.0       33.6  454.366654   
2934                  41    7.0         68.0       36.7  453.351155   
2935                  40   73.0         71.0       39.8   57.348340   
2936                  39   76.0         75.0       42.1  548.587312   
2937                  39   78.0         78.0       43.5  547.358878   

       thinness  1-19 years   thinness 5-9 years  \
0                      17.2                 17.3   
1                      17.5                 17.5   
2                      17.7                 17.7   
3                      17.9                 18.0   
4                      18.2                 18.2   
...                     ...                  ...   
2933                    9.4                  9.4   
2934                    9.8                  9.9   
2935                    1.2                  1.3   
2936                    1.6                  1.7   
2937                   11.0                 11.2   

      Income composition of resources  Schooling  
0                               0.479       10.1  
1                               0.476       10.0  
2                               0.470        9.9  
3                               0.463        9.8  
4                               0.454        9.5  
...                               ...        ...  
2933                            0.407        9.2  
2934                            0.418        9.5  
2935                            0.427       10.0  
2936                            0.427        9.8  
2937                            0.434        9.8  

[1649 rows x 14 columns] 0       65.0
1       59.9
2       59.9
3       59.5
4       59.2
        ... 
2933    44.3
2934    44.5
2935    44.8
2936    45.3
2937    46.0
Name: Life expectancy , Length: 1649, dtype: float64

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
X_train,X_test,Y_train,Y_test = train_test_split(X.values,Y.values,test_size=0.2) #dataset is split in the 4:1 ratio for training and testing

model=LinearRegression()
model.fit(X_train,Y_train) #(training) fiting the data to the dataset
print(model.score(X_train,Y_train)) #r2 score
print(model.score(X_test,Y_test)) #print the R2 score for both the training and testing sets to evaluate the model's performance.

0.8289517081052937
0.812440597177055

life_expectancy_coeff = pd.DataFrame(model.coef_,X.columns,columns=['Coefficient'])
life_expectancy_coeff #Understanding the coefficients helps to interpret the impact of each feature on the predicted outcome.

	Coefficient
Adult Mortality	-0.018759
Alcohol	-0.139051
percentage expenditure	0.000403
Hepatitis B	-0.003710
BMI	0.033776
under-five deaths	-0.001319
Polio	0.008982
Diphtheria	0.016367
HIV/AIDS	-0.414523
GDP	0.000018
thinness 1-19 years	0.035633
thinness 5-9 years	-0.068861
Income composition of resources	10.633458
Schooling	0.960030

model.intercept_

52.25524864107931

predictions = model.predict(X_test) #make predictions on the test set

plt.scatter(Y_test,predictions) # visualize the predicted values against the actual values using a scatter plot

<matplotlib.collections.PathCollection at 0x7e0c1bba6920>

coefficients = pd.DataFrame(data=model.coef_.reshape(-1,1),index=X.columns,columns=["coefficients"]) #create a DataFrame to show the coefficients for each feature
print(coefficients)
print("Intercept:", model.intercept_) #print the intercept
print("Function: \n", "y = " + " +\n".join([f"({val:.2f})*({X.columns[ind]})" for ind,val in enumerate(model.coef_)]) + f" +\n({model.intercept_})") #print the linear regression equation

                                 coefficients
Adult Mortality                     -0.018759
Alcohol                             -0.139051
percentage expenditure               0.000403
Hepatitis B                         -0.003710
 BMI                                 0.033776
under-five deaths                   -0.001319
Polio                                0.008982
Diphtheria                           0.016367
 HIV/AIDS                           -0.414523
GDP                                  0.000018
 thinness  1-19 years                0.035633
 thinness 5-9 years                 -0.068861
Income composition of resources     10.633458
Schooling                            0.960030
Intercept: 52.25524864107931
Function: 
 y = (-0.02)*(Adult Mortality) +
(-0.14)*(Alcohol) +
(0.00)*(percentage expenditure) +
(-0.00)*(Hepatitis B) +
(0.03)*( BMI ) +
(-0.00)*(under-five deaths ) +
(0.01)*(Polio) +
(0.02)*(Diphtheria ) +
(-0.41)*( HIV/AIDS) +
(0.00)*(GDP) +
(0.04)*( thinness  1-19 years) +
(-0.07)*( thinness 5-9 years) +
(10.63)*(Income composition of resources) +
(0.96)*(Schooling) +
(52.25524864107931)

# MAE MSE RMSE
from sklearn import metrics
print('MAE1:', metrics.mean_absolute_error(Y_test, predictions))
print('MSE1:', metrics.mean_squared_error(Y_test, predictions))
print('RMSE1:', np.sqrt(metrics.mean_squared_error(Y_test, predictions)))

MAE1: 3.0756719082362913
MSE1: 16.037107579841344
RMSE1: 4.004635761194936

import statsmodels.api as sm
from scipy import stats

X_ = sm.add_constant(X_train)
est = sm.OLS(Y_train, X_)
est2 = est.fit()
print(est2.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.829
Model:                            OLS   Adj. R-squared:                  0.827
Method:                 Least Squares   F-statistic:                     451.4
Date:                Sun, 21 Jan 2024   Prob (F-statistic):               0.00
Time:                        18:12:45   Log-Likelihood:                -3556.8
No. Observations:                1319   AIC:                             7144.
Df Residuals:                    1304   BIC:                             7221.
Df Model:                          14                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         52.2552      0.785     66.602      0.000      50.716      53.794
x1            -0.0188      0.001    -17.405      0.000      -0.021      -0.017
x2            -0.1391      0.034     -4.145      0.000      -0.205      -0.073
x3             0.0004      0.000      1.985      0.047    4.65e-06       0.001
x4            -0.0037      0.005     -0.726      0.468      -0.014       0.006
x5             0.0338      0.007      5.051      0.000       0.021       0.047
x6            -0.0013      0.001     -1.883      0.060      -0.003     5.5e-05
x7             0.0090      0.006      1.525      0.127      -0.003       0.021
x8             0.0164      0.007      2.444      0.015       0.003       0.030
x9            -0.4145      0.021    -20.020      0.000      -0.455      -0.374
x10         1.827e-05   3.22e-05      0.568      0.570   -4.49e-05    8.14e-05
x11            0.0356      0.058      0.609      0.542      -0.079       0.150
x12           -0.0689      0.058     -1.197      0.232      -0.182       0.044
x13           10.6335      0.957     11.113      0.000       8.756      12.511
x14            0.9600      0.067     14.318      0.000       0.828       1.092
==============================================================================
Omnibus:                       40.658   Durbin-Watson:                   2.006
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               66.118
Skew:                          -0.263   Prob(JB):                     4.39e-15
Kurtosis:                       3.963   Cond. No.                     1.22e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.22e+05. This might indicate that there are
strong multicollinearity or other numerical problems.

col_mask = (est2.pvalues[1:])<0.05

X.columns[col_mask]

Index(['Adult Mortality', 'Alcohol', 'percentage expenditure', ' BMI ',
       'Diphtheria ', ' HIV/AIDS', 'Income composition of resources',
       'Schooling'],
      dtype='object')

col_mask2 = np.logical_not(col_mask)
X.columns[col_mask2]

Index(['Hepatitis B', 'under-five deaths ', 'Polio', 'GDP',
       ' thinness  1-19 years', ' thinness 5-9 years'],
      dtype='object')

#life_expectancy.drop(['Polio','Hepatitis B','GDP',' thinness  1-19 years','under-five deaths ',' thinness 5-9 years'],axis=1,inplace=True)
life_expectancy.head(1)

	Life expectancy	Adult Mortality	Alcohol	percentage expenditure	BMI	Diphtheria	HIV/AIDS	Income composition of resources	Schooling
0	65.0	263.0	0.01	71.279624	19.1	65.0	0.1	0.479	10.1

X2=life_expectancy.drop('Life expectancy ',axis=1)
Y2=life_expectancy['Life expectancy ']
print(X2,Y2)

      Adult Mortality  Alcohol  percentage expenditure   BMI   Diphtheria   \
0               263.0     0.01               71.279624   19.1         65.0   
1               271.0     0.01               73.523582   18.6         62.0   
2               268.0     0.01               73.219243   18.1         64.0   
3               272.0     0.01               78.184215   17.6         67.0   
4               275.0     0.01                7.097109   17.2         68.0   
...               ...      ...                     ...    ...          ...   
2933            723.0     4.36                0.000000   27.1         65.0   
2934            715.0     4.06                0.000000   26.7         68.0   
2935             73.0     4.43                0.000000   26.3         71.0   
2936            686.0     1.72                0.000000   25.9         75.0   
2937            665.0     1.68                0.000000   25.5         78.0   

       HIV/AIDS  Income composition of resources  Schooling  
0           0.1                            0.479       10.1  
1           0.1                            0.476       10.0  
2           0.1                            0.470        9.9  
3           0.1                            0.463        9.8  
4           0.1                            0.454        9.5  
...         ...                              ...        ...  
2933       33.6                            0.407        9.2  
2934       36.7                            0.418        9.5  
2935       39.8                            0.427       10.0  
2936       42.1                            0.427        9.8  
2937       43.5                            0.434        9.8  

[1649 rows x 8 columns] 0       65.0
1       59.9
2       59.9
3       59.5
4       59.2
        ... 
2933    44.3
2934    44.5
2935    44.8
2936    45.3
2937    46.0
Name: Life expectancy , Length: 1649, dtype: float64

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
X2_train,X2_test,Y2_train,Y2_test = train_test_split(X2.values,Y2.values,test_size=0.2)

model2=LinearRegression()
model2.fit(X2_train,Y2_train)
print(model.score(X2_train,Y2_train)) #r2 score
print(model.score(X2_test,Y2_test))

0.8243791898208145
0.8209650654574213

life_expectancy_coeff2 = pd.DataFrame(model2.coef_,X2.columns,columns=['Coefficient'])
life_expectancy_coeff2

	Coefficient
Adult Mortality	-0.018239
Alcohol	-0.094395
percentage expenditure	0.000447
BMI	0.040110
Diphtheria	0.020884
HIV/AIDS	-0.476124
Income composition of resources	9.661914
Schooling	1.012723

model2.intercept_

51.68852172103817

predictions2 = model2.predict(X2_test)

plt.scatter(Y2_test,predictions2)

<matplotlib.collections.PathCollection at 0x7e0c15a03af0>

coefficients2 = pd.DataFrame(data=model2.coef_.reshape(-1,1),index=X2.columns,columns=["coefficients"]) #create a DataFrame to show the coefficients for each feature
print(coefficients2)
print("Intercept:", model2.intercept_) #print the intercept
print("Function: \n", "y = " + " +\n".join([f"({val:.2f})*({X2.columns[ind]})" for ind,val in enumerate(model2.coef_)]) + f" +\n({model2.intercept_})")

                                 coefficients
Adult Mortality                     -0.018239
Alcohol                             -0.094395
percentage expenditure               0.000447
 BMI                                 0.040110
Diphtheria                           0.020884
 HIV/AIDS                           -0.476124
Income composition of resources      9.661914
Schooling                            1.012723
Intercept: 51.68852172103817
Function: 
 y = (-0.02)*(Adult Mortality) +
(-0.09)*(Alcohol) +
(0.00)*(percentage expenditure) +
(0.04)*( BMI ) +
(0.02)*(Diphtheria ) +
(-0.48)*( HIV/AIDS) +
(9.66)*(Income composition of resources) +
(1.01)*(Schooling) +
(51.68852172103817)

X_2 = sm.add_constant(X2_train)
est2_2 = sm.OLS(Y2_train, X_2)
est22 = est2_2.fit()
print(est22.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.826
Model:                            OLS   Adj. R-squared:                  0.825
Method:                 Least Squares   F-statistic:                     776.7
Date:                Sun, 21 Jan 2024   Prob (F-statistic):               0.00
Time:                        18:17:55   Log-Likelihood:                -3585.5
No. Observations:                1319   AIC:                             7189.
Df Residuals:                    1310   BIC:                             7236.
Df Model:                           8                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         51.6885      0.687     75.234      0.000      50.341      53.036
x1            -0.0182      0.001    -16.895      0.000      -0.020      -0.016
x2            -0.0944      0.034     -2.808      0.005      -0.160      -0.028
x3             0.0004   6.46e-05      6.916      0.000       0.000       0.001
x4             0.0401      0.006      6.519      0.000       0.028       0.052
x5             0.0209      0.005      4.305      0.000       0.011       0.030
x6            -0.4761      0.023    -21.136      0.000      -0.520      -0.432
x7             9.6619      0.916     10.550      0.000       7.865      11.459
x8             1.0127      0.066     15.373      0.000       0.883       1.142
==============================================================================
Omnibus:                       37.110   Durbin-Watson:                   2.029
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               62.228
Skew:                          -0.230   Prob(JB):                     3.07e-14
Kurtosis:                       3.960   Cond. No.                     1.76e+04
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.76e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

col_mask2 = (est22.pvalues[1:])<0.05
print(col_mask2)

[ True  True  True  True  True  True  True  True]

print('MAE2:', metrics.mean_absolute_error(Y2_test, predictions2))
print('MSE2:', metrics.mean_squared_error(Y2_test, predictions2))
print('RMSE2:', np.sqrt(metrics.mean_squared_error(Y2_test, predictions2)))

MAE1: 2.8738818423360657
MSE1: 14.660168731913682
RMSE1: 3.828859978102318

D={
    'Model name':['Model 1','Model 2'],
    'Independent Variables': ['Adult Mortality, Alcohol, percentage expenditure, Hepatitis B, BMI, under-five deaths, Polio, Diphtheria, HIV/AIDS, GDP, thinness  1-19 years, thinness 5-9 years, Income composition of resources, Schooling','Adult Mortality, Alcohol, percentage expenditure, BMI, Diphtheria, HIV/AIDS, Income composition of resources, Schooling'],
    'MAE':['3.0756719082362913','2.8738818423360657'],
    'MSE':['16.037107579841344','14.660168731913682'],
    'RMSE':['4.004635761194936','3.828859978102318'],
    'R_SQ':['0.812440597177055','0.8209650654574213']
}

DF = pd.DataFrame(data=D)
DF

	Model name	Independent Variables	MAE	MSE	RMSE	R_SQ
0	Model 1	Adult Mortality, Alcohol, percentage expenditu...	3.0756719082362913	16.037107579841344	4.004635761194936	0.812440597177055
1	Model 2	Adult Mortality, Alcohol, percentage expenditu...	2.8738818423360657	14.660168731913682	3.828859978102318	0.8209650654574213

Life Expectancy Prediction: Multiple Linear Regression Model

Vrushali Kadam - 22BLC1300

Objective:

The objective of this analysis is to build and evaluate a linear regression model for predicting life expectancy based on a given dataset. This involves comprehensive data preprocessing, exploratory data analysis (EDA), and the application of a linear regression model with subsequent evaluation.

Data Loading and Exploration:

We initiated the analysis by loading the life expectancy dataset using Pandas:

import pandas as pd

life_expectancy = pd.read_csv('/content/Life Expectancy Data.csv') life_expectancy.dropna(inplace=True)

Subsequently, we inspected the dataset by examining data types, and providing a statistical summary:

life_expectancy.dtypes life_expectancy.describe()

Data Preprocessing:

To streamline the dataset for linear regression modeling, we removed irrelevant columns ('Country' and 'Status'):

life_expectancy.drop(['Country', 'Status'], inplace=True, axis=1)

Exploratory Data Analysis (EDA):

EDA was performed to better understand relationships within the data. We created a correlation heatmap and a pair plot:

import matplotlib.pyplot as plt import seaborn as sns

def make_corr_heatmap(df): corr = df.corr() fig, ax = plt.subplots(figsize=(12, 9)) sns.heatmap(corr, annot=True) ax.set_xticklabels(ax.get_xticklabels()) plt.show()

make_corr_heatmap(life_expectancy) sns.pairplot(life_expectancy, diag_kind='kde')

Methodology:

Linear Regression Modeling:

The dataset was split into training and testing sets, and a linear regression model was trained using scikit-learn:

from sklearn.model_selection import train_test_split from sklearn.linear_model import LinearRegression

X = life_expectancy.drop('Life expectancy ', axis=1) Y = life_expectancy['Life expectancy ']

X_train, X_test, Y_train, Y_test = train_test_split(X.values, Y.values, test_size=0.2) model = LinearRegression() model.fit(X_train, Y_train)

Model Evaluation and Coefficients:

The model's performance was evaluated using R2 score,MAE,MSE,RMSE. Additionally, we examined the coefficients and intercept of the linear regression model:

For Model 1:

print(model.score(X_train, Y_train)) print(model.score(X_test, Y_test))

life_expectancycoeff = pd.DataFrame(model.coef, X.columns, columns=['Coefficient']) print(life_expectancy_coeff)

from sklearn import metrics print('MAE1:', metrics.mean_absolute_error(Y_test, predictions)) print('MSE1:', metrics.mean_squared_error(Y_test, predictions)) print('RMSE1:', np.sqrt(metrics.mean_squared_error(Y_test, predictions)))

Similarly is done for the Model 2 as well

Results:

We limited the number of models to two due to the significant p-values obtained for all variables in the second model. Model 2 emerges as the optimal choice among various models, providing insights into the impact of relevant independent variables on life expectancy. It serves as the most accurate representation of the data, offering the optimal equation for Multiple Linear Regression.

#RESULTS

DF

	Model name	Independent Variables	MAE	MSE	RMSE	R_SQ
0	Model 1	Adult Mortality, Alcohol, percentage expenditu...	3.0756719082362913	16.037107579841344	4.004635761194936	0.812440597177055
1	Model 2	Adult Mortality, Alcohol, percentage expenditu...	2.8738818423360657	14.660168731913682	3.828859978102318	0.8209650654574213

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